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Testing Mean Reversion in Fund Returns with a Lagged Regression

Article Quant Q&A · Author: T-T
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Summary

The document considers whether monthly fund returns can be modeled as mean reverting and whether an Ornstein–Uhlenbeck process is suitable. The response cautions that fitting a mean-reversion model to returns assumes past returns help predict future returns, an assumption that may be weak in many datasets. It suggests that financial fundamentals, such as valuation multiples, may be more likely to exhibit mean reversion than returns themselves.

As a simple empirical check, it proposes regressing next-period returns on current-period returns. A negative slope would be consistent with mean reversion, but the fit should also be examined. The answer expects the relationship to explain little even if the estimated coefficient is negative. No dataset, regression results, or formal OU estimation procedure is supplied, so the suggestion is a starting point for investigation rather than evidence that a particular fund’s returns mean revert or a forecast of when reversal will occur.

Key ideas

  • A mean-reversion model on returns assumes historical returns predict future returns.
  • Fundamentals such as valuation multiples may be more plausible mean-reverting variables than returns.
  • Regressing next-period returns on current returns offers a basic test for return mean reversion.
  • A negative regression coefficient alone is insufficient; the fit also matters.

Tags

Mean reversionStatisticsFixed income
Full text
# R Mean Reversion Estimate on Funds


# R Mean Reversion Estimate on Funds












I am new to mean reversion, and I'd like to run an analysis on a fund (ts with monthly returns only) to see if mean reversion applies and if so, when it will happen.

Most of the examples I found focus on cointegrated securities. Ornstein-Uhlenbeck seems to be a popular model for mean reversion estimate. If someone could please provide me an example of applying OU model on a return-only time series or point me to the right direction, I will really appreciate it!

## Answer by NYC07 (score 1)

https://quant.stackexchange.com/a/36970

T, while not necessarily a direct answer to your question, I just wanted to offer a word of caution in applying a mean reversion model to security or fund returns.

In attempting to fit a mean reversion model to returns, you are implicitly stating that you believe that historical returns are good predictors of future returns. Although I don't know what your dataset is, this is generally not the case.

More likely to be mean reverting are the fundamentals underlying these returns. Using a financial markets example this might be something like multiples (P/E or EV/EBITDA).

But if you still wanted to run such a mean reversion analysis, I would recommend starting with a regression with a format similar to the following: use as your independent (x) variable the returns from period t and as your dependent (y) variable the returns from period t+1. If there is mean reversion you should see a negative resulting coefficient, although you should also check the fit of your result as well -- in keeping with my comments above, I would expect the fit to be poor, even if your coefficient is negative.

Hope this helps!

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.